On the Koenigs function of semigroups of holomorphic self-maps of the unit disc

Let $$(\phi _t)$$(ϕt) be a semigroup of holomorphic self-maps of $$\mathbb {D}$$D. In this note, we use an abstract approach to define the Koenigs function of $$(\phi _t)$$(ϕt) and “holomorphic models” and show how to deduce the existence and properties of the infinitesimal generator of $$(\phi _t)$$(ϕt) from this construction.